I have an assignment on predicate logic and while I understand my notes when I'm reading them, applying those notes to the questions I'm being asked isn't working so well. I've got a couple different solutions to this question and I don't know if it's right.
Formulate the following sentences into predicate logic:
a) There are lawyers who only respect lawyers. L(x) is a lawyer and R(x,y) x respects y.
I've come up with two different answers but I'm not sure which one is right.
$\exists x \exists y(L(x) \land L(y) \land R(x,y))$
$\exists x \exists y ((L(y) \land R(x,y)) \implies L(x))$
And this one I'm not even sure how to start.
e) Everyone's mother is respected, if she is a strong woman. Use mother(x) = x's mother, not mother(x,y). R(x,y) x respects y, W(x) x is a woman, S(x) x is strong. I had an answer but it doesn't look right...
$\forall x \exists y(W(y) \land S(y) \land mother(x)) \implies R(x,y)$